Primal-Dual Neural Algorithmic Reasoning

TL;DR

This paper introduces a neural algorithmic reasoning framework based on primal-dual methods, enabling neural networks to approximate and outperform classical algorithms on complex graph problems with strong generalization.

Contribution

It presents a novel primal-dual inspired neural algorithmic reasoning framework that extends NAR to harder problems and demonstrates superior performance and practical utility.

Findings

Outperforms classical approximation algorithms on multiple tasks

Shows strong generalization to larger and out-of-distribution graphs

Successfully integrates with commercial solvers for real-world datasets

Abstract

Neural Algorithmic Reasoning (NAR) trains neural networks to simulate classical algorithms, enabling structured and interpretable reasoning over complex data. While prior research has predominantly focused on learning exact algorithms for polynomial-time-solvable problems, extending NAR to harder problems remains an open challenge. In this work, we introduce a general NAR framework grounded in the primal-dual paradigm, a classical method for designing efficient approximation algorithms. By leveraging a bipartite representation between primal and dual variables, we establish an alignment between primal-dual algorithms and Graph Neural Networks. Furthermore, we incorporate optimal solutions from small instances to greatly enhance the model's reasoning capabilities. Our empirical results demonstrate that our model not only simulates but also outperforms approximation algorithms for multiple tasks, exhibiting robust generalization to larger and out-of-distribution graphs. Moreover, we highlight the framework's practical utility by integrating it with commercial solvers and applying it to real-world datasets.